Update statistics in conservative parallel-discrete-event simulations of asynchronous systems

We model the performance of an ideal closed chain of L processing elements that work in parallel in an asynchronous manner. Their state updates follow a generic conservative algorithm. The conservative update rule determines the growth of a virtual time surface. The physics of this growth is reflected in the utilization (the fraction of working processors) and in the interface width. We show that it is possible to make an explicit connection between the utilization and the microscopic structure of the virtual time interface. We exploit this connection to derive the theoretical probability distribution of updates in the system within an approximate model. It follows that the theoretical lower bound for the computational speedup is $s=(L+1\mathrm{})/4\mathrm{}$ for $L>~4.$ Our approach uses simple statistics to count distinct surface-configuration classes consistent with the model growth rule. It enables one to compute analytically microscopic properties of an interface, which are unavailable by continuum methods.